Independent Erasure Channels Research Articles

Plant and buffer state estimation for networked predictive control over multiple erasure channels

This paper investigates optimal estimation for networked control systems composed of linear, time-variant, and multi-input multi-output (MIMO) plants that communicate with the controller over multiple independent erasure channels. In the controller-to-plant link, we cope with data losses by considering a networked predictive control strategy in which the controller not only sends the current control inputs to the actuators, but also sequences of predicted control inputs at every time step. These are stored in buffers located at the corresponding actuator side, with the aim of being used in case of data loss. Additionally, for losses occurring in the plant-to-controller link, we assume that the controller contains a data-dropout compensation mechanism capable of replacing the missing measurements with their optimal estimates. It is assumed that acknowledgment packages are sent from the plant to the controller, to indicate if the previous sequence was received or not. For this setup, we compute optimal time-varying estimates of the plant and buffer state, and for the lost measurements as well. Finally, we provide the optimal stationary estimator, which serves as a simpler alternative to the time-varying one.

Delay on Broadcast Erasure Channels Under Random Linear Combinations

We consider a transmitter broadcasting random linear combinations (over a field of size $d$) formed from a block of $c$ packets to a collection of $n$ receivers, where the channels between the transmitter and each receiver are independent erasure channels with reception probabilities $\mathbf{q} = (q_1,\ldots,q_n)$. We establish several properties of the random delay until all $n$ receivers have recovered all $c$ packets, denoted $Y_{n:n}^{(c)}$. First, we provide lower and upper bounds, exact expressions, and a recurrence for the moments of $Y_{n:n}^{(c)}$. Second, we study the delay per packet $Y_{n:n}^{(c)}/c$ as a function of $c$, including the asymptotic delay (as $c \to \infty$), and monotonicity (in $c$) properties of the delay per packet. Third, we employ extreme value theory to investigate $Y_{n:n}^{(c)}$ as a function of $n$ (as $n \to \infty$). Several results are new, some results are extensions of existing results, and some results are proofs of known results using new (probabilistic) proof techniques.

Multi-Party Secret Key Agreement Over State-Dependent Wireless Broadcast Channels

We consider a group of $m$ trusted and authenticated nodes that aim to create a shared secret key $K$ over a wireless channel in the presence of an eavesdropper Eve. We assume that there exists a state-dependent wireless broadcast channel from one of the honest nodes to the rest of them including Eve. All of the trusted nodes can also discuss over a cost-free, noiseless and unlimited rate public channel which is also overheard by Eve. For this setup, we develop an information-theoretically secure secret key agreement protocol. We show the optimality of this protocol for “linear deterministic” wireless broadcast channels. This model generalizes the packet erasure model studied in the literature for wireless broadcast channels. Here, the main idea is to convert a deterministic channel into multiple independent erasure channels by using superposition coding. For “state-dependent Gaussian” wireless broadcast channels, by using insights from the deterministic problem, we propose an achievability scheme based on a multi-layer wiretap code. By using the wiretap code, we can mimic the phenomenon of converting the wireless channel into multiple independent erasure channels. Then, finding the best achievable secret key generation rate leads to solving a non-convex power allocation problem over these channels (layers). We show that using a dynamic programming algorithm, one can obtain the best power allocation for this problem. Moreover, we prove the optimality of the proposed achievability scheme for the regime of high-SNR and large-dynamic range over the channel states in the (generalized) degrees of freedom sense.

Optimal control over multiple erasure channels using a data dropout compensation scheme

In this paper we focus on networked control systems subject to data dropouts. We consider that the controller communicates with the plant through multiple independent erasure channels, and that each actuator sends acknowledgement packages to the controller. We restrict our attention to the optimal design of a class of controllers that embeds a data dropout compensator and where, besides this compensation mechanism, all processing is an affine function of the available data. Our first result shows that the optimal design consists in solving, separately, an estimation problem and a control problem. The optimal controller is a linear function of the estimated state, which is obtained exploiting the information given by the acknowledgement packages and the data dropout compensator. Since we focus on a specific class of controllers, our proposal is suboptimal, however, unlike the optimal LQG controller found in the literature, our proposal is easier to implement, and its steady state behaviour can be simply determined. We also show that, under standard conditions, the affine part of the optimal controller converges to an LTI filter, which can be used as a simple alternative to the time varying controller.

<sc>xor</sc>-Based Encoding With Instantaneous Decoding for the Broadcast Erasure Channel With Feedback: The Three-User Case

We study the case of a three-user broadcast erasure channel with multiple unicast traffic sessions, where feedback from the users is fed back to the transmitter in the form of positive acknowledgment (ACK)/negative acknowledgment (NACK) messages. The capacity region of this system has been recently derived and two capacity-achieving coding algorithms employing intersession linear network coding have been proposed. Since these algorithms suffer from large computational complexity and decoding delay, our aim, in this paper, is to design a coding algorithm with reduced computational complexity and a low decoding delay that achieves a comparable rate region to the former algorithms. We exclusively consider algorithms that require no knowledge of channel statistics, only perform XOR operations among the packets, and allow for instantaneous decoding by any receiver that successfully receives a packet. We present such an algorithm, named IXOR, which operates on a specially constructed network of virtual queues and, through intelligent packet combining, achieves the capacity under a general condition, which is satisfied in the following settings: 1) spatially independent identically distributed erasure channels with arbitrary values of erasure probability, and 2) spatially independent erasure channels where the maximum erasure probability does not exceed 8/9.

Throughput-Delay Analysis of Random Linear Network Coding for Wireless Broadcasting

In an unreliable single-hop broadcast network setting, we investigate the throughput and decoding-delay performance of random linear network coding as a function of the coding window size and the network size. Our model consists of a source transmitting packets of a single flow to a set of $n$ users over independent erasure channels. The source performs random linear network coding (RLNC) over $k$ (coding window size) packets and broadcasts them to the users. We note that the broadcast throughput of RLNC must vanish with increasing $n$, for any fixed $k.$ Hence, in contrast to other works in the literature, we investigate how the coding window size $k$ must scale for increasing $n$. Our analysis reveals that the coding window size of $\Theta(\ln(n))$ represents a phase transition rate, below which the throughput converges to zero, and above which it converges to the broadcast capacity. Further, we characterize the asymptotic distribution of decoding delay and provide approximate expressions for the mean and variance of decoding delay for the scaling regime of $k=\omega(\ln(n)).$ These asymptotic expressions reveal the impact of channel correlations on the throughput and delay performance of RLNC. We also show how our analysis can be extended to other rateless block coding schemes such as the LT codes. Finally, we comment on the extension of our results to the cases of dependent channels across users and asymmetric channel model.

Online XOR packet coding: Efficient single-hop wireless multicasting with low decoding delay

In this paper we present a cross-layer solution to the problem of unreliability in IEEE 802.11 wireless multicast network, where an Access Point (AP) is multicasting a data file to a group of receivers over independent wireless erasure channels. We first present a practical scheme for collecting feedback frames from the receivers by means of simultaneous acknowledgment (ACK) frames collision. Based on these feedback frames, we design an online linear XOR coding algorithm to retransmit the lost packets. Through simulation results we first show that our proposed coding algorithm outperforms all the existing XOR coding algorithms in terms of retransmission rate. We further show that our proposed coding algorithm has the lowest average decoding delay of all the known network coding schemes. XOR coding and decoding only requires addition over GF(2), hence it enjoys lower encoding and decoding computational complexities. Because of these features such an online XOR coding algorithm is also of interest for delay-sensitive applications such as multicast audio video (AV) streaming, and in battery constrained devices such as smartphones.

ARQ-Based Symmetric-Key Generation Over Correlated Erasure Channels

This paper focuses on the problem of sharing secret keys using Automatic Repeat reQuest (ARQ) protocol. We consider cases where forward and feedback channels are erasure channels for a legitimate receiver (Bob) and an eavesdropper (Eve). In prior works, the wiretap channel is modeled as statistically independent packet erasure channels for Bob and Eve. In this paper, we go beyond the state-of-the-art by addressing correlated erasure events across the wiretap channel. The created randomness is shared between two legitimate parties through ARQ transmissions that is mapped into a destination set using a first-order digital filter with feedback. Then, we characterize Eve's information loss about this shared destination set, due to inevitable transmission errors. This set is then transformed into a highly secure key using privacy amplification in order to intensify and exploit Eve's lack of knowledge. We adopt two criteria for analysis and design of the system: secrecy outage probability as a measure of the secrecy quality, and secret key rate as a metric for efficiency. The resulting secrecy improvement is presented as a function of the correlation coefficients and the erasure probabilities for both channels. It is shown that secrecy improvement is achievable even when Eve has a better channel than legitimate receivers, and her channel conditions are unknown to legitimate users.

Efficient Algorithms for Optimal Uneven Protection of Single and Multiple Scalable Code Streams Against Packet Erasures

we study algorithmic approaches for rate-fidelity optimal packetization of a single and multiple scalable source code streams with uneven erasure protection (UEP). A new algorithm is developed to obtain the globally optimal solution for scalable source codes of convex rate-fidelity function and for a wide class of erasure channels, including channels for which the probability of losing packets is monotonically nonincreasing in , and independent erasure channels with packet erasure rate smaller than 0.5. This is achieved at linear space complexity and near-linear time complexity in the transmission budget, representing significant improvement over the known globally optimal algorithm. When applied to SPIHT compressed images, the results of the proposed algorithm are virtually the same as the global optima. The above success is also extended to UEP packetization of multiple scalable code streams. We improve the existing algorithms in both speed and performance.

Globally Optimal Uneven Error-Protected Packetization of Scalable Code Streams

In this paper, we present a family of new algorithms for rate-fidelity optimal packetization of scalable source bit streams with uneven error protection. In the most general setting where no assumption is made on the probability function of packet loss or on the rate-fidelity function of the scalable code stream, one of our algorithms can find the globally optimal solution to the problem in O(N/sup 2/L/sup 2/) time, compared to a previously obtained O(N/sup 3/L/sup 2/) complexity, where N is the number of packets and L is the packet payload size. If the rate-fidelity function of the input is convex, the time complexity can be reduced to O(NL/sup 2/) for a class of erasure channels, including channels for which the probability function of losing n packets is monotonically decreasing in n and independent erasure channels with packet erasure rate no larger than N/2(N + 1). Furthermore, our O(NL/sup 2/) algorithm for the convex case can be modified to rind an approximation solution for the general case. All of our algorithms do away with the expediency of fractional bit allocation, a limitation of some existing algorithms.